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Simplifying 64x2 + -48x = 375 Reorder the terms: -48x + 64x2 = 375 Solving -48x + 64x2 = 375 Solving for variable 'x'. Reorder the terms: -375 + -48x + 64x2 = 375 + -375 Combine like terms: 375 + -375 = 0 -375 + -48x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -5.859375 + -0.75x + x2 = 0 Move the constant term to the right: Add '5.859375' to each side of the equation. -5.859375 + -0.75x + 5.859375 + x2 = 0 + 5.859375 Reorder the terms: -5.859375 + 5.859375 + -0.75x + x2 = 0 + 5.859375 Combine like terms: -5.859375 + 5.859375 = 0.000000 0.000000 + -0.75x + x2 = 0 + 5.859375 -0.75x + x2 = 0 + 5.859375 Combine like terms: 0 + 5.859375 = 5.859375 -0.75x + x2 = 5.859375 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 5.859375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 5.859375 + 0.140625 Combine like terms: 5.859375 + 0.140625 = 6 0.140625 + -0.75x + x2 = 6 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -0.375) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -0.375 = 2.449489743 Simplifying x + -0.375 = 2.449489743 Reorder the terms: -0.375 + x = 2.449489743 Solving -0.375 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.449489743 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.449489743 + 0.375 x = 2.449489743 + 0.375 Combine like terms: 2.449489743 + 0.375 = 2.824489743 x = 2.824489743 Simplifying x = 2.824489743Subproblem 2
x + -0.375 = -2.449489743 Simplifying x + -0.375 = -2.449489743 Reorder the terms: -0.375 + x = -2.449489743 Solving -0.375 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.449489743 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.449489743 + 0.375 x = -2.449489743 + 0.375 Combine like terms: -2.449489743 + 0.375 = -2.074489743 x = -2.074489743 Simplifying x = -2.074489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.824489743, -2.074489743}
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